question_answer 5)

                An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression \[c=2\pi r,\] where r is the radius of the circle.                 (a)                    (b)           (c)

Answer:

                (a) Perimeter of the food piece \[=\pi \left( \frac{2.8}{2} \right)cm+2.8\,cm\] \[=\frac{22}{7}\times 1.4\,cm\,+2.8\,cm\] \[=4.4\,cm+2.8\,cm\]  = 7.2 cm (b) Perimeter of the food piece = 2.8 cm + 1.5 cm + 1.5 cm \[+\pi \left( \frac{2.8}{2} \right)cm\] \[=5.8\,cm+\frac{22}{7}\,\times 1.4\,cm\] \[5.8\text{ }cm+4.4\text{ }cm\] = 10.2 cm (c) Perimeter of the food piece \[=2\,cm+2\,cm\,+\pi \,\left( \frac{2.8}{2} \right)\,cm\] \[=4\,cm+\frac{22}{7}\,\times 1.4\,cm\] = 4 cm + 4.4 cm = 8.4cm Therefore, the ant would have to take a longer round for food piece (&).